Question

The equation of the stationary wave is $y=2A\sin \left(\frac{2\pi ct}{\lambda }\right)\cos \left(\frac{2\pi x}{\lambda }\right)$ Which of the following statements is wrong?

• A. The unit of $ct$ is same as that of $\lambda$
• B. The unit of $x$ is same as that of $\lambda$
• C. The unit of $2\pi c/\lambda$ is same as that of $2\pi x/\lambda t$
• D. The unit of $c/\lambda$ is same as that of $x/\lambda$

Answer 1

Answer: (D)

Here, $(2\pi ct/\lambda )$ as well $(2\pi x/\lambda )$ are dimensionless.
So, unit of $ct$ is same as that of $\lambda$ and unit of $x$ is same as that of $\lambda <br>$ Since, $\left[\frac{2\pi ct}{\lambda }\right]=\left[\frac{2\pi x}{\lambda }\right]=[M^0{L}^0{T}^0]$
$\therefore$ $\frac{2\pi c}{\lambda }=\frac{2\pi x}{\lambda t}$
In the option , $\frac{x}{\lambda }$ is unit less.
It is not the case with $c/\lambda$ .